Finite Group Databasebeta

← #30610475

Subgroups — #30610475

Order 15616.

1248 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C211yesmaximal, characteristic, complemented
2C2×#16840783C211yesmaximal, characteristic, complemented
3#21461163C212yesmaximal, complemented
4#21461160C212yesmaximal, complemented
5#21461152C214yesmaximal, complemented
6#21461116C214yesmaximal, complemented
7C2×#16840230C211yesmaximal, characteristic
8#16840783—21no—
9#16840783—21no—
10#16840783—21no—
11#16840783C2212yes—
12#16840783C2212yescomplemented
13#16840782—21no—
14#16840779C2212yescomplemented
15#16840778C2212yescomplemented
16#16840765—21no—
17C2×C4⋊#92420C2212yescomplemented
18#16840732—21no—
19C2×C22⋊#92420—21no—
20C4×#11758217C2212yes—
21C2×#14519832—21no—
22#16840612C2218yescomplemented
23#16840610C2218yescomplemented
24C22×#11758222C411yescharacteristic
25#16840230—21no—
26#16840230—21no—
27#16840230—21no—
28#16840230—21no—
29#16840230C412yes—
30#16840230C412yes—
31#16840230C2212yes—
32#16840230C2212yes—
33C2×#14519742C411yescharacteristic
34C2×#14519742C2211yescharacteristic
35C2×#14519739C411yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×#14519737—21no—
38C2×#14519737—21no—
39C2×#14519734—21no—
40C22×C4×Dic61C2211yescharacteristic
41C2×C42×D61—21no—
42C2×#117×C61C411yescharacteristic
43C2×#11758217—22no—
44C22×#92420—22no—
45#14519844—22no—
46C4⋊#92420—22no—
47C4⋊#92420—22no—
48C4⋊#92420C2314yes—
49C22⋊#92420—22no—
50C22⋊#92420—22no—
51C22⋊#92420—22no—
52C22⋊#92420—22no—
53#14519832—22no—
54#14519832—22no—
55#14519832—22no—
56C4×#92420C2314yes—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—28no—
60C2×#11758222C2×C412yes—
61C2×#11758222C2×C412yes—
62C22×Dic122C2×C411yescharacteristic
63C22×D244C2×C411yescharacteristic
64C22×C22⋊D61—21no—
65C23×Dic61D411yescharacteristic
66C23×Dic61D411yescharacteristic
67C22×C4×D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61—21no—
70#14519742—21no—
71#14519742—21no—
72#14519742—21no—
73#14519742—21no—
74#14519742C2×C412yes—
75#14519742C2×C412yes—
76#14519742C2×C412yes—
77#14519742C2312yes—
78#14519739—21no—
79#14519739—21no—
80#14519739—21no—
81#14519739—21no—
82#14519739C2×C412yes—
83#14519739C2×C412yes—
84#14519739C2×C412yes—
85#14519739C2312yes—
86#14519737—22no—
87#14519737—22no—
88#14519737—22no—
89#14519737—22no—
90#14519737—22no—
91#14519737—22no—
92#14519737—22no—
93#14519737—22no—
94#14519734—22no—
95#14519734—22no—
96#14519734—22no—
97#14519734—22no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116C42×D61—22no—
117C42×D61—22no—
118C42×D61—22no—
119C42×D61—22no—
120C23×C4×C61C2×C411yescharacteristic
121#117×C61—21no—
122#117×C61—21no—
123#117×C61C2×C412yes—
124#117×C61C2×C412yes—
125C2×C4⋊C4×C61C2×C411yescharacteristic
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C42×C61—21no—
129C24×C61C22⋊C411yescharacteristic
130C23×D61—21no—
131C22×C4×C61—24no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61C22⋊C411yescharacteristic
135C22×C4×C61C22⋊C411yescharacteristic
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C2×C22⋊D61—28no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C22×Dic61—21no—
144C22×Dic61—42no—
145C22×Dic61—42no—
146C22×Dic61C22⋊C411yescharacteristic
147C22×Dic61C22⋊C411yescharacteristic
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22⋊C411yescharacteristic
150C22×Dic61C22⋊C411yescharacteristic
151C22×Dic61C22⋊C411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158#11758222—28no—
159#11758222—28no—
160#11758222—24no—
161#11758222—24no—
162#11758222—24no—
163#11758222M1618yescomplemented
164C2×D244—21no—
165C2×D244—24no—
166C2×D244C22×C412yes—
167C2×C4×D61—28no—
168C2×C4×D61—22no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—44no—
175C2×C4×D61—44no—
176C2×Dic122—21no—
177C2×Dic122—24no—
178C2×Dic122C22×C412yes—
179#11758217—44no—
180C2×#92420—24no—
181C2×#92420—24no—
182C2×#92420—44no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61C22×C412yes—
186C4⋊C4×C61C22×C412yes—
187C22⋊C4×C61—22no—
188C22⋊C4×C61—22no—
189C42×C61—22no—
190C42×C61—22no—
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199C4×Dic61—22no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61C22⋊C411yescharacteristic
204C4×Dic61C22⋊C411yescharacteristic
205C4×Dic61C22⋊C411yescharacteristic
206C4×Dic61C22⋊C411yescharacteristic
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22×C411yescharacteristic
210C4×Dic61C22×C411yescharacteristic
211C4×Dic61C22×C411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61C2×D411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2411yescharacteristic
219C23×C61—22no—
220C23×C61—22no—
221C23×C61—41no—
222C23×C61C2×C22⋊C411yescharacteristic
223C23×C61C2×C22⋊C411yescharacteristic
224C23×C61C2×C22⋊C411yescharacteristic
225C22×D61—24no—
226C22×D61—22no—
227C22×D61—42no—
228C22×D61—42no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×M1614yes—
242C2×C4×C61C23×C411yescharacteristic
243C22⋊D61—28no—
244C22⋊D61—28no—
245C2×Dic61—24no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61C2×C22⋊C411yescharacteristic
260C2×Dic61C2×C22⋊C411yescharacteristic
261C2×Dic61C2×C22⋊C411yescharacteristic
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61C22×D411yescharacteristic
266C2×Dic61C22×D411yescharacteristic
267D244—24no—
268D244—22no—
269D244C2×M1614yes—
270C4×D61—28no—
271C4×D61—28no—
272C4×D61—44no—
273C4×D61—44no—
274C4×D61—44no—
275C4×D61—44no—
276Dic122—24no—
277Dic122—22no—
278Dic122C2×M1614yes—
279#92420—44no—
280#92420—44no—
281#17452—611nomaximal, Sylow
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—44no—
290C22×C61#40712yes—
291C22×C61#42112yes—
292C22×C61C22×C22⋊C411yescharacteristic
293C2×D61—24no—
294C2×D61—48no—
295C2×D61—42no—
296C2×D61—42no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—42no—
300C4×C61—42no—
301C4×C61#40712yes—
302C4×C61C22×M1612yes—
303Dic61—24no—
304Dic61—21no—
305Dic61—21no—
306Dic61—21no—
307Dic61—21no—
308Dic61—21no—
309Dic61—21no—
310Dic61—21no—
311Dic61#57512yes—
312C2×C4×#41—611no—
313#2920—611no—
314C2×#432—611no—
315#1491—612no—
316#1490—612no—
317#1488—614no—
318#1477—614no—
319C2×C61—22no—
320C2×C61—22no—
321C2×C61—41no—
322C2×C61C2×#40711yescharacteristic
323C2×C61#289611yescharacteristic
324C2×C61C2×#42111yescharacteristic
325D61—44no—
326C22×#41—611no—
327C4×#41—612no—
328C4×#41—612no—
329C4×#41—612no—
330C4×#41—612no—
331C4×#41—1221no—
332C4×#41—1221no—
333C4×#41—1221no—
334C4×#41—1221no—
335C2×C4×Q8—611no—
336C2×C4×Q8—611no—
337C2×C4×D4—611no—
338C2×C4×D4—611no—
339C2×C4×D4—1221no—
340C2×C4×D4—1221no—
341C2×#117—1221no—
342C2×#117#692311yescharacteristic
343C22×C42—611no—
344C22×C42—1221no—
345#432—612no—
346#432—612no—
347#432—1221no—
348#432—1221no—
349#432—1221no—
350#432—1221no—
351#431—612no—
352#431—612no—
353#423—1221no—
354C2×C4⋊C8—612no—
355#407—1221no—
356C2×C22⋊C8—1221no—
357C4×M16—612no—
358C2×#97—1221no—
359Q8⋊C8—618no—
360D4⋊C8—618no—
361C61#1745211yescharacteristic, complemented, Sylow
362C2×#41—612no—
363C2×#41—612no—
364C2×#41—1228no—
365C2×#41—1221no—
366C2×#41—1221no—
367C22×Q8—611no—
368C22×D4—611no—
369C22×D4—1221no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—1221no—
373C23×C4—1221no—
374C23×C4—1221no—
375C23×C4C2×#692311yescharacteristic
376C2×M16—1222no—
377C22×C8—1222no—
378C4×Q8—612no—
379C4×Q8—612no—
380C4×Q8—612no—
381C4×Q8—612no—
382C4×Q8—1221no—
383C4×Q8—1221no—
384C4×Q8—1221no—
385C4×Q8—1221no—
386C4×D4—612no—
387C4×D4—612no—
388C4×D4—612no—
389C4×D4—612no—
390C4×D4—1221no—
391C4×D4—1221no—
392C4×D4—1221no—
393C4×D4—1221no—
394C4×D4—1222no—
395C4×D4—1222no—
396C4×D4—1222no—
397C4×D4—1222no—
398C4×D4—1222no—
399C4×D4—1222no—
400C4×D4—1222no—
401C4×D4—1222no—
402#117—21no—
403#117—21no—
404#117—1222no—
405#117—1222no—
406#117—1222no—
407#117—1222no—
408#117C2×#692312yes—
409#117C2×#692312yes—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4C2×#692311yescharacteristic
413C2×C4⋊C4C2×#692311yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C42—21no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—1222no—
431C2×C42—1222no—
432C2×C42—1222no—
433C2×C42—1222no—
434C2×C42—1221no—
435C2×C42—1221no—
436C4⋊C8—614no—
437C4⋊C8—1222no—
438C4⋊C8—1222no—
439C4⋊C8—1222no—
440C22⋊C8—1222no—
441C22⋊C8—1222no—
442C22⋊C8—1222no—
443C22⋊C8—1222no—
444#97—1222no—
445#97—1222no—
446#97—1222no—
447C4×C8—614no—
448C24—1221no—
449C24C22⋊#692311yescharacteristic
450#41—618no—
451#41—1224no—
452#41—1224no—
453#41—1228no—
454#41—1228no—
455#41—1224no—
456C2×Q8—612no—
457C2×Q8—1224no—
458C2×Q8—1221no—
459C2×D4—612no—
460C2×D4—1224no—
461C2×D4—1228no—
462C2×D4—1222no—
463C2×D4—1222no—
464C2×D4—1221no—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1228no—
485C22×C4—1221no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—2444no—
489C22×C4—2444no—
490C22×C4—2442no—
491C22×C4—2442no—
492C22×C4C22⋊#692311yescharacteristic
493C22×C4C22⋊#692311yescharacteristic
494C22×C4C22⋊#692311yescharacteristic
495C22×C4C22×#692311yescharacteristic
496C22×C4C22×#692311yescharacteristic
497C22×C4C22×#692311yescharacteristic
498M16—2444no—
499C2×C8—1224no—
500C2×C8—1224no—
501C2×C8—2444no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4C22×#692312yes—
509C4⋊C4C22×#692312yes—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—1222no—
513C22⋊C4—1222no—
514C22⋊C4—1222no—
515C22⋊C4—1222no—
516C42—22no—
517C42—22no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—1222no—
535C42—1222no—
536C42—1222no—
537C42—1222no—
538C23—22no—
539C23—22no—
540C23—41no—
541C23—1224no—
542C23—1222no—
543C23—2442no—
544C23—2442no—
545C23C2×C22⋊#692311yescharacteristic
546C23C2×C22⋊#692311yescharacteristic
547C23C2×C22⋊#692311yescharacteristic
548Q8—614no—
549Q8—1224no—
550Q8—1222no—
551D4—614no—
552D4—1224no—
553D4—1228no—
554D4—1228no—
555D4—1222no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—611no—
566C2×C4—611no—
567C2×C4—611no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—1228no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1224no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1228no—
582C2×C4—2444no—
583C2×C4—2444no—
584C2×C4—2444no—
585C2×C4—2444no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4C2×C22⋊#692311yescharacteristic
594C2×C4C2×C22⋊#692311yescharacteristic
595C2×C4C2×C22⋊#692311yescharacteristic
596C2×C4D61⋊M1614yes—
597C2×C4C23×#692311yescharacteristic
598C8—2444no—
599C8—2444no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—44no—
608C22—1224no—
609C22—2448no—
610C22—2442no—
611C22—2442no—
612C22#1684073412yes—
613C22#1684075912yes—
614C22C22×C22⋊#692311yescharacteristic
615C4—21no—
616C4—21no—
617C4—42no—
618C4—42no—
619C4—612no—
620C4—1224no—
621C4—1221no—
622C4—1221no—
623C4—1221no—
624C4—1221no—
625C4—1221no—
626C4—1221no—
627C4—1221no—
628C4#1684073412yes—
629C4C2×D61⋊M1612yes—
630C2—22no—
631C2—22no—
632C2—41no—
633C2—2444no—
634C2C2×#1684073411yescharacteristic
635C2#2146243911yescharacteristic
636C2C2×#1684075911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#117×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758222C4
cosocleC4×Dic61C24
hypercenterC2×#117#6923
hypocenterC61#17452
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21462495C2semidirect
2. C2×#16840783C2semidirect
3. #21461163C2semidirect
4. #21461160C2semidirect
5. #21461152C2semidirect
6. #21461116C2semidirect
12. #16840783C22semidirect
14. #16840779C22semidirect
15. #16840778C22semidirect
17. C2×C4⋊#92420C22semidirect
22. #16840612C22semidirect
23. #16840610C22semidirect
163. #11758222M16semidirect
361. C61#17452semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214624952
C2×#168407832
#214611632
#214611602
#214611522
#214611162
C2×#168402302
#1745261